Understanding the influence of environment on baryonic processes is a fundamental goal in studies of galaxy evolution, and galaxy clusters offer ideal laboratories with which to examine environmental effects on their constituent members. Clusters continually evolve and build up mass through the accumulation of galaxies, resulting in distinct galaxy populations based on their accretion history. I will discuss using cluster phase space (line-of-sight velocity versus projected clustercentric radius) as a way to probe the accretion histories of cluster galaxies to study environmental effects on star formation at z~1. I will also present recent ALMA observations of massive gas reservoirs in z=1.6 cluster galaxies. The raw fuel of star formation, molecular gas is typically absent in low-redshift cluster galaxies; with these new ALMA data, we are witnessing the first direct evidence that gas-rich galaxies are located indistinguishably in both the field and clusters at high-redshift.